Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption

TL;DR

This paper reviews recent theoretical advances in understanding wave scattering in chaotic and disordered systems with absorption, deriving analytic expressions for reflection distributions and exploring implications for localization and impedance correlations.

Contribution

It introduces a supersymmetric sigma-model approach to analyze non-unitary scattering matrices and provides new analytic results for reflection and impedance statistics in disordered systems.

Findings

Derived closed-form expressions for reflection probability distributions.

Established statistical independence between phase and modulus of reflection amplitudes.

Analyzed the role of absorption as an indicator of Anderson localization.

Abstract

We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric sigma-model, we are able to derive closed form analytic expressions for the distribution of reflection probability in a generic disordered system. One of the most important properties resulting from such an analysis is statistical independence between the phase and the modulus of the reflection amplitude in every perfectly open channel. The developed theory has far-reaching consequences for many quantities of interest, including local Green functions and time delays. In particular, we point out the role played by absorption as a sensitive indicator of mechanisms behind the Anderson localisation transition. We also provide a random-matrix-based analysis of S-matrix and impedance correlations for various symmetry classes as well as the distribution of transmitted power for systems with broken time-reversal invariance, completing previous works on the subject. The results can be applied, in particular, to the experimentally accessible impedance and reflection in a microwave or ultrasonic cavity attached to a system of antennas.